Absolutely weak abs can affect squatting and deadlifting. You're wanting to know what you can do about it right? My answer is going to seem like overkill but I think it's necessary to understand all of this if you really want the right answer to your question. This stuff is kind of hard to grasp but I'll do my best to explain:
The sheer fact that you have to ask this question of whether or not your abs can affect your deadlift tells me something. It tells me you lack consciousness and/or muscle activation in the lower abs, groin or hips because if you had that, then you wouldn't need to ask the question that you did because you would simply be able to move your hips/abs around and answer the question yourself. That's alright though, that is where everyone starts. What I mean by consciousness is consciousness over a sense called proprioception. Proprioception is the sense of your muscles. More specifically it serves as a feedback mechanism for us to learn more efficient ways of controlling ourselves (coordination). In your case, you probably don't have a good perception of your lower abs and that's why you lack muscle activation there.
The whole point of exercise is to consciously change proprioception. To make an extremely long story short, there are multiple ways of perceiving what is seemingly the same physical movement and that is what the central nervous system is ultimately responsible for in the context of exercise. The central nervous system is simply your brain and therefore it is a matter of psychology. It is responsible for the psychology of human movement perception (kinesthesia). For example, when you are squatting, some people perceive the situation as lowering the weight down as they squat down and then moving the weight back up. Coming from that perspective, they are focusing on moving the weight. Typically this type of psychology is used in strength training. However, some people perceive the situation as the ability to postulate their body while being held under a weight or tension. They don't perceive the weight as going up and down, they simply perceive the situation as being able to control their posture in the manner they choose (squatting up and down) while being under a weight. This type of psychology is more conducive to coordination. The difference between these two is that they have different focal points and that dictates how they perceive the situation. These subtle differences account for the differences in how we are coordinated. Strength and coordination are your two main athletic characteristics. Or in other words, how your neurons are wired together (coordination) and the strength of those connections (strength). Do you see how you two people can do what is seemingly the same thing but get drastically different results? Most people on this forum call that "genetics" but actually it's not. It's all sports psychology.
To give you a small piece of advice on sports psychology, imagine that your brain and body are two separate entities. Typically you think of your brain and body together as representing yourself but from now on think of your brain as you and your body is just an entity that surrounds you in which you have control over. Coming from that perspective might help you to achieve better coordination as it will teach you to be more conscious of proprioception.
Without moving too much, try to locate your lower abs in 3D space. (locating things in 3d space is actually the mechanism of how your brain uses proprioception, your brain does not discriminate against muscles, it does not know of muscles, it only knows of locating things in 3d space). Slightly tense them, just very lightly and do it a few times including your obliques and experiment with the different ways you can control them. What you're doing is concentrating on proprioception which is what your mind should be focusing on during coordination training. Coordination training comes before strength training. Just because you are able to go through a physical motion does not mean you are coordinated. Coordination is not discrete, it's continuous. In other words, it's not something you either have or don't have but rather it's something that can always be improved. Coordination is the fluency of your movements at a very micro level. Where you lack coordination is so minute, small and obscure that you won't be able to identify it. That's the point of doing repetitions. Higher and lower repetitions are the fundamental difference between strength and coordination training. Higher repetitions are more conducive to motor learning (coordination) and lower repetitions with heavier weights are more conducive to strength training.
Going back to your question, you want to know what you can do to "strengthen" your abs. I would say highly repetitious movements where you focus on muscle activation in the lower abs such as a set of 100 situps. Try doing a hundred situps every day or every other day to build coordination. 100 is just a ballpark number. Then you can slowly transition to strength training by adding weight. As for the exercises, that's actually another complicated subject of exercise design and choosing the right exercise for you. To keep it simple though, just do your traditional ab exercises like situps, leg raises, knee ups etc.... I know this was a lot of information but if I don't explain the psychological component you're always going to struggle to make progress. Your average person will never figure this stuff out. Just remember it's all psychological. Ask questions if you have them or if you like I can keep explaining more if I haven't lost you already.
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